In the circuit configuration of a piezoelectric oscillator which is a type that changes an oscillation frequency by using a Variable Capacitance Diode, as summarized in a Voltage Controlled Crystal Oscillator (VCXO) on pages 17 to 18 in “Description and Application of Crystal Device (March, 2002)” published by QIAJ (Quartz Crystal Industry Association of Japan), for example, a variable capacitance diode is inserted in an oscillation loop, and a control voltage is externally applied to the variable capacitance diode, whereby a capacitance of the variable capacitance diode is changed. Accordingly, a load capacitance of the oscillation loop is changed so that the frequency is varied.
FIG. 5 shows an example of a circuit in a generally used voltage controlled crystal oscillator, which is also disclosed, for example, in Japanese Patent Application Laid-Open No. 09-214250. An inverter element IC1 is used in the oscillation circuit. A high resistance R1 is inserted between an input and an output of the inverter element IC1, so that an operating point is always set to the center. Between the input and the output of the inverter element IC1, a crystal unit Xtal, and a variable capacitance unit in which a condenser C5 is connected in parallel to a variable capacitance diode D1 are inserted in series, thereby configuring an oscillation loop. The parallel connection of the condenser C5 to the variable capacitance diode D1 allows a variable range to be controlled finely. Furthermore, condensers C1 and C2 are respectively inserted between GND and the input of the inverter element IC1 and between GND and the output thereof.
An external control voltage Vcont is divided by high resistances R2 and R3, and is applied to a cathode of the variable capacitance diode D1. An anode of the variable capacitance diode D1 is connected to GND through a high resistance R4. A capacitance is changed by the voltage between the cathode and the anode of the variable capacitance diode D1, so that a load capacitance of the oscillation loop is changed. As a result, an oscillation frequency is changed. The variable width and the linearity of the frequency can be controlled finely by the high resistance R3 and an element value of the condenser C5.
FIG. 6 is another conventional example used for a high-frequency oscillation, in which two transistors (TR1, TR2) are cascade-connected in an oscillation circuit. Two variable capacitance diodes D1 and D2 are connected in series so as to prevent deterioration in noise characteristic caused by self-modulating due to an oscillating level.
Conventionally, a frequency offset at the time of capacitance loading of the piezoelectric oscillation circuit is approximately given by Equation (1) as DL (=Fractional Load Resonance Frequency Offset). The equivalent circuit model therefor is shown in FIG. 7. A load capacitance of the oscillation loop (=CL) can be expressed as a configuration in which a circuit load (=Cc) and a variable capacitance (=Cx) are connected in series.
                                                                        D                L                            ⁡                              (                                  C                  x                                )                                      ≈                                          1                                  2                  ⁢                                                                          ⁢                  γ                                            ⨯                              1                                  1                  +                                                            C                      L                                                              C                      0                                                                                                    ∵                      1                          C              L                                      =                              1                          C              x                                +                      1                          C              c                                                          (        1        )            
By setting a reference capacitance (=CLref) that gives a nominal frequency, the frequency offset can be expressed by Equation (2).
                                          D            Lref                    ⁡                      (                          C              x                        )                          ≈                              1                          2              ⁢              γ                                ⨯                      1                          1              +                                                C                  Lref                                                  C                  0                                                                                        (        2        )            
ΔDL, an amount of change in frequency from the nominal frequency, is a difference calculated by subtracting Equation (2) from Equation (1). This can be expressed by Equations (3) and (4).
                              Δ          ⁢                                          ⁢                                    D              L                        ⁡                          (                              C                x                            )                                      ≈                                            D              L                        ⁡                          (                              C                x                            )                                -                                    D              Lref                        ⁡                          (                              C                x                            )                                                          (        3        )                                                                                                      Δ                  ⁢                                                                          ⁢                                                            D                      L                                        ⁡                                          (                                              C                        x                                            )                                                                      ≈                                ⁢                                                      1                                          2                      ⁢                      γ                                                        ⁢                                      {                                                                  1                                                  1                          +                                                      1                                                                                          C                                0                                                            ⁡                                                              (                                                                                                      1                                                                          C                                      x                                                                                                        +                                                                      1                                                                          C                                      c                                                                                                                                      )                                                                                                                                                        -                                              1                                                  1                          +                                                                                    C                              Lref                                                                                      C                              0                                                                                                                                            }                                                                                                                                           ⁢                                                      ∵                                                                  C                        L                                                                    C                        0                                                                              =                                                            1                                                                        C                          0                                                                          C                          L                                                                                      =                                          1                                                                        C                          0                                                ⁡                                                  (                                                                                    1                                                              C                                x                                                                                      +                                                          1                                                              C                                c                                                                                                              )                                                                                                                                                        ⁢                                  ⁢                  γ          ⁢                      :                    ⁢                                          ⁢          Capacitance          ⁢                                          ⁢                      Ratio            ⁡                          (                                                =                                ⁢                                  C                  0                                ⁢                                  /                                ⁢                                  C                  1                                            )                                                          (        4        )            
Examples of variable capacitance characteristics of the variable capacitance diode are shown in FIGS. 8 and 9. As is apparent from FIGS. 8 and 9, the variable characteristics of the variable capacitance diode can be approximated by Equation (5), and the variable capacitance Cx is obtained in Equation (6).Vari(ν)=α×e−nv  (5)                α: Capacitance when applied voltage is zero        n: GradientCX=Vari(ν)+Cb  (6)        Cb: Parallel capacitance of variable capacitance        
Substitution of Equation (4) into Equation (6) provides Equation (7), which is a relational expression showing a frequency change and a variable voltage applied by an external control voltage to the variable capacitance diode.
                              Δ          ⁢                                          ⁢                                    D              L                        ⁡                          (                              C                ⁡                                  (                  v                  )                                            )                                      ≈                              1                          2              ⁢              γ                                ⁢                      {                                          1                                  1                  +                                      1                                                                  C                        0                                            ⁡                                              (                                                                              1                                                                                          αⅇ                                                                  -                                  nv                                                                                            +                                                              C                                b                                                                                                              +                                                      1                                                          C                              c                                                                                                      )                                                                                                        -                              1                                  1                  +                                                            C                      Lref                                                              C                      0                                                                                            }                                              (        7        )            
Equation (8) for giving a linear frequency change with respect to the variable voltage is shown blow.
                                                                                          Δ                  ⁢                                                                          ⁢                                                            D                      L                                        ⁡                                          (                                              C                        ⁡                                                  (                          v                          )                                                                    )                                                                      ≈                                ⁢                                                      1                                          2                      ⁢                      γ                                                        ⁢                                      {                                                                  1                                                  1                          +                                                      1                                                                                          C                                0                                                            ⁡                                                              (                                                                                                      1                                                                          C                                      ⁡                                                                              (                                        v                                        )                                                                                                                                              +                                                                      1                                                                          C                                      c                                                                                                                                      )                                                                                                                                                        -                                              1                                                  1                          +                                                                                    C                              Lref                                                                                      C                              0                                                                                                                                            }                                                                                                                                            =                                    ⁢                                                            1                                              2                        ⁢                        γ                                                              ⁢                                          {                                              A                        ⁡                                                  (                                                      v                            -                            a                                                    )                                                                    )                                                                      }                                                    ⁢                                  ⁢                  A          ⁢                      :                    ⁢                                          ⁢          Gradient          ⁢                                          ⁢          of          ⁢                                          ⁢          frequency                ⁢                                  ⁢                  with          ⁢                                          ⁢          respect          ⁢                                          ⁢          to          ⁢                                          ⁢          variable          ⁢                                          ⁢          voltage                ⁢                                  ⁢                              a            ⁢                          :                        ⁢                                                  ⁢            Voltage            ⁢                                                  ⁢            for            ⁢                                                  ⁢                                          Δ                ⁢                D                            L                                =                      0            ⁢                                                  ⁢            by            ⁢                                                  ⁢            nominal            ⁢                                                  ⁢            frequency                                              (        8        )            
Equation (9) obtained by modifying Equation (8) is shown below. Equation (9) gives the linear frequency change with respect to the variable voltage.
                              C          ⁡                      (            v            )                          =                  1                                                    1                                  C                  0                                            ⁢                              1                                                      1                                                                                            A                          ⁡                                                      (                                                          v                              -                              a                                                        )                                                                          )                                            +                                              1                                                  1                          +                                                                                    C                              Lref                                                                                      C                              0                                                                                                                                                            -                  1                                                      -                          1                              C                c                                                                        (        9        )            
FIG. 10 shows examples of simulation results of Equations (5), (6) and (9).
The crystal unit Xtal is At-Cut, and a resonance frequency thereof is 13 MHz. It should be noted that Co=1.35 pF, γ=277, and the circuit capacitance Cc is 60 pF. Furthermore, the 3 variable voltage is Vcont±2.5Vdc, and the variable width is ΔDL±45 ppm.
The variable capacitance C(v) for obtaining a straight line is a curve in which the variable capacitance C(v) is approximately equal to 11.8 pF at 0V, and is approximately equal to 7.5 pF at 5V. A combined capacitance of a variable capacitance diode Vbari and a parallel capacitance Cb that show a characteristic very close to that of the same capacitance change is expressed by Equation (10).11.02×e−0.097ν+0.6[pF]  (10)
The difference in capacitance between the C(v) in this case and the combined capacitance of the variable capacitance diode is approximately equal to or less than 0.3 pF at maximum.
FIG. 11 shows a variable capacitance C(v) for obtaining a straight line, a frequency change by an approximate variable capacitance diode by the combined capacitance, and a difference therebetween. A difference of 1 ppm provides a change of 70 ppm in width. This value is expected to be a value that indicates a compensation limit by the variable capacitance diode.
The results shown in FIG. 12 indicate a capacitance difference in between an ideal capacitance change and an approximate variable capacitance diode, and a frequency deviation by the capacitance difference.
An outline of contents of FIG. 12 is shown in FIG. 13. That is, the most appropriate selection of an “ideal capacitance change for obtaining a straight line” and a “capacitance change of the variable capacitance diode” that follows a log change results in intersections at two points, P1 and P2. This indicates that the optimum characteristic can be obtained in the vicinity thereof, and indicates also a compensation limit.
Patent Document 1: Japanese Patent Application Laid-Open No. 09-214250
Patent Document 2: Japanese Patent Application Laid-Open No. 10-056330
As shown in FIGS. 12 and 13, In conventional frequency control by single-direction voltage control to a variable capacitance diode, there is a limit in an amount of correction for obtaining a straight line.